Question

If a^x=b^y=c^z and y=(xz)^1/2 , find the value of loga*logc/(logb)^2

Answer 1

a^x=b^y=c^z

apply log on all sides

and let it equals to k

hence , xloga=ylogb=zlogc=k

loga=k/x, logb=k/y, logc=k/z

substitute in loga*logc/(logb)^2

((k/x)*(k/z)) / (k^2/y^2)

cancel k^2

then, y^2/x*z

but its given that it equals 1 hence,

loga*logc/(logb)^2 = 1

Answer 2

Answer:

1

will be the answer of the above question.